Score : 800 points
There is a tree with N vertices numbered 1 through N.
The i-th edge connects Vertex x_i and y_i.
Each vertex is painted white or black.
The initial color of Vertex i is represented by a letter c_i.
c_i = W
represents the vertex is white; c_i = B
represents the vertex is black.
A cat will walk along this tree. More specifically, she performs one of the following in one second repeatedly:
The cat's objective is to paint all the vertices black. She may start and end performing actions at any vertex. At least how many seconds does it takes for the cat to achieve her objective?
W
or c_i = B
.Input is given from Standard Input in the following format:
N x_1 y_1 x_2 y_2 : x_{N-1} y_{N-1} c_1c_2..c_N
Print the minimum number of seconds required to achieve the objective.
5 1 2 2 3 2 4 4 5 WBBWW
5
The objective can be achieved in five seconds, for example, as follows:
6 3 1 4 5 2 6 6 1 3 4 WWBWBB
7
1 B
0
20 2 19 5 13 6 4 15 6 12 19 13 19 3 11 8 3 3 20 16 13 7 14 3 17 7 8 10 20 11 9 8 18 8 2 10 1 6 13 WBWBWBBWWWBBWWBBBBBW
21